1. Field of the Invention
The present invention relates to a method and an apparatus for controlling or determining and estimating an object system which controls or determines, in order to obtain, for example, predetermined distribution concerning a function characteristic distribution of an object such as magnetic flux distribution and temperature distribution, a parameter for specifying an object such as shape and a physical value of the material and also estimates an internal condition of the object such as a physical value of the material on the basis of a measured value obtained for the object.
2. Description of the Prior Art
FIG. 27 is a flowchart explaining a method for obtaining the predetermined uniform magnetic flux distribution by optimizing the shape of an electromagnet explained on page 393 of the Proceedings of Electric Society in Japan, A No. 9, Vol. 109 (1989). FIG. 28 shows a model under the bidimensional analysis of an electromagnet as an object.
In FIG. 28, the reference numeral 90 denotes a coil to which a current is applied to generate a magnetic field in the gap 93 of a magnetic body 91 and poles 92 of the electromagnet. In this case, the magnetic field distribution in the gap 93 is determined by the shape of the poles 92. Therefore, it is desired to obtain a shape of the poles 92 which unifies as much as possible the magnetic flux density in the y direction of evaluation region 94 enclosed by a dotted line in the gap 93. Now, the electromagnet is assumed to be placed within the air region.
Operations will then be explained. In this case, the shape of poles 92 is a parameter which specifies an object and the predetermined function characteristic distribution is a uniform magnetic field distribution. Moreover, a boundary element method is used as an analysis method in the above reference. The boundary element method is used for analyzing the characteristics of a complicated analysis object through a division of elements on the boundary using the boundary element equation.
First, the initial condition is set (step ST51). This includes setting of the initial condition means, setting of coordinates of each node and setting of physical values of a material in each boundary element when the analysis object is divided into a finite number of boundary elements. In this case, the initial shape of poles 92 is set to a flat shape as shown in FIG. 20(a).
Next, a target value in the finite number of evaluating points i (i=1, . . . , M) within the evaluating region 94, namely a value of the predetermined uniform magnetic field in this case, is set (step ST52). Next, a y element of the magnetic field in the M evaluating points is calculated by the boundary element method (step ST53). Moreover, a sum of the squares of the errors between the calculated values and the target values in the M evaluating points is calculated and error evaluation is conducted for this sum of the squares (step ST 54).
When an error is the predetermined value or less, processing is completed and if not, calculation of the evaluating function described in the above reference is conducted (step ST56). In addition, the amount of correction of the shape of poles 92 is determined by using the calculation result of the evaluating function (step ST55). The boundary element analysis is executed again for the corrected shape to calculate the y element in the evaluating point (step ST53).
The shape of poles 92 is converted to that suitable for predetermined uniform magnetic field distribution by repeating the processings of the steps ST 53 to ST 55 several times, namely repeating the boundary element analysis as explained above. FIG. 29 shows a converging process of the shape of poles 92. In this figure, (a).about.(f) show the shape of poles 92 corresponding to the number of times of repetition of the boundary element analysis. Namely, these illustrations show a profile where a relative error of the generated magnetic field for the target magnetic field is reduced with the increase in the number of times of repetition.
FIG. 30 illustrates a sectional view of a cross-sectional model of the chest portion of a human body for obtaining the distribution of conductivity within a human body described in the IEEE Transaction on Biomedial Engineering, Vol. BME-32, No. 3, 1985). A method of obtaining the distribution of conductivity within a human body is an example of a method for estimating an internal condition of an object from the measured values of the object. In this case, distribution of conductivity shows an internal condition of an object.
The chest portion of a human body includes lungs (dotted regions in FIG. 30) and conductivity is largely different in the spaces. Therefore, as shown in FIG. 30, when a current is applied externally, distribution of the conductivity within a human body can be estimated by measuring voltages generated at the surface of a human body at many points. It is called a impedance CT problem.
For the processings, the interior of a human body is divided into triangular elements as shown in FIG. 30 and the conductivity of each element is supposed as .sigma.i (i=1, . . . , M). The processing procedures are similar to that shown in the flowchart of FIG. 27. First, the initial condition is set. Namely, the coordinates of each node 101.about.120 is set and a node to which a current is applied is determined. For example, it is assumed that a current is applied across the nodes 101 and 111. Moreover, the initial value of the conductivity .sigma.i of each element is set.
Next, potential values at the surface of a human body, namely potential values at the nodes 102.about.110, 111.about.120 are computed. The finite element method is an approximate solution method in which an interior analysis of an object having a complicated shape and distribution of physical value is divided into finite number of elements and a physical condition assigned to each element is calculated based on the principle of energy minimization. As a result of the analysis by the finite element method, the potential at each node can be computed in this case.
Here, an error between the computed node potential and the actually measured node potential is evaluated. If an error exceeds the predetermined value, the conductivity .sigma.i (i=1, . . . , M) of each element is corrected using the evaluation result and analysis by the finite element method is executed again using the corrected conductivity .sigma.i of each element. Moreover, such processings are repeated until an error between the computed node potential and the measured node potential becomes the predetermined value or less, for example, until a sum of the squares of the error becomes the predetermined value or less.
FIG. 31 shows a profile where a mean value of estimated errors, namely a mean value of the error between the computed node potential and the measured node potential is reduced as the number of times of repetition of analysis by the finite element method increases.
Since a conventional method and apparatus for controlling or determining and estimating an object system is configured as explained above, if the initial condition (the initial shape or distribution of initial physical value) is largely deviated from the final condition (final shape or distribution of true physical value), such method and apparatus shows a problem that the number of times of repetitive computation of the boundary element method and finite element method increases and the time rquired until the final condition is obtained becomes longer. It is because the time required for single execution of the boundary element method and finite element method is considerably longer.
Moreover, there lies a problem that it is probable that the processing will be completed, in the error evaluation, before the true error is minimized when many local minimum values exist. For example, as shown in FIG. 32, when a parameter value at the point C is employed as the initial value of the parameter which specifies an object, an error can be set to the minimum true value. However, when a parameter value at the point A or B is employed as the initial value, an erroneous parameter is determined as the parameter in the final condition.